O(log log n) time algorithms for Hamiltonian-suffix and min-max-pair heap operations on hypercube multicomputers

Abstract

We present an efficient mapping of a min-max-pair heap of size N on a hypercube multicomputer of p processors in such a way the load on each processor's local memory is balanced and no additional communication overhead is incurred for implementation of the single insertion, deletemin and deletemax operations. Our novel approach is based on an optimal mapping of the paths of a binary heap into a hypercube such that in O(log N/p+log p) time we can compute the Hamiltonian-suffix, which is defined as a pipelined suffix-minima computation on an O(log N)length heap path embedded into the Hamiltonian path of the hypercube according to the binary reflected Gray codes. However the binary tree underlying the heap data structure is not altered by the mapping process.